LINEAR CONTROL SYSTEMS Ali Karimpour Assistant Professor Ferdowsi University of Mashhad

Lecture 18 Ali Karimpour Nov Lecture 18 Time domain design of control systems Topics to be covered include: v Effect of moving poles and zeros. v Design of controller in time domain. u Various controller configurations. u Different kind of controllers. u Controller realization.

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها Consider following equation: Let b=1 but a=10, 9, 8, 3, 1

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها Let a=10

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها Let a=9

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها Let a=8

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها -3 Let a=3

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها Let a=1

Lecture 18 Ali Karimpour Nov Effect of moving poles. اثرات حرکت قطبها a=10 a= 9 a= a= 3 -3 a= 1

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت + - r(t) e(t) u(t) c(t) Controller Controlled process 1 Series or cascade compensation. 1 ساختار کنترلی سری

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت 2 Feedback compensation. 2 جبران سازی فیدبکی + - r(t) e(t) u(t) c(t) )(sG p + - Controlled process Controller

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت 3 State-feedback control. 3 کنترل فیدبک حالت + - r(t) u(t) x(t) )(sG p c(t) Controlled process Controller

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت 4Series-feedback compensation. (Two degree of freedom) 4 جبران سازی سری فیدبکی ( دو درجه آزادی ) + - r(t) e(t) u(t) c(t) )(sG p + - Controlled process Controller Compensation

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت 5 Forward compensation with series compensation. (Two degree of freedom) 5 جبران سازی پیش رو با جبران سازی سری ( دو درجه آزادی ) + - r(t) e(t) u(t) c(t) )(sG p Controlled process Controller

Lecture 18 Ali Karimpour Nov Various controller configurations. ساختارهای کنترلی متفاوت 6 Feed forward compensation. (Two degree of freedom) 6 کنترلر پیش خور ( دو درجه آزادی ) + r(t) e(t) u(t) c(t) )(sG p Controller Controlled process

Lecture 18 Ali Karimpour Nov Series Compensation Structure In this Course consider the simple SISO control loop shown in the figure. جبران سازی سری Controller Series or cascade compensation. ساختار کنترلی سری There is a lot of different controller!

Lecture 18 Ali Karimpour Nov In This course انواع کنترلر Different kind of controllers PID controllers. Lead lag controllers H 2 Controllers H ∞ Controllers Intelligent Controllers ………….. Adaptive Controllers NN Controllers ………….. Different kind of controllers In Graduate courses

Lecture 18 Ali Karimpour Nov PID Controllers PID has become almost universally used in industrial control. These controllers have proven to be robust and extremely beneficial in the control of many important applications. PID stands for:P (Proportional) I (Integral) D (Derivative) کنترلر PID

Lecture 18 Ali Karimpour Nov Historical Note Early feedback control devices implicitly or explicitly used the ideas of proportional, integral and derivative action in their structures. However, it was probably not until Minorsky’s work on ship steering * published in 1922, that rigorous theoretical consideration was given to PID control. This was the first mathematical treatment of the type of controller that is now used to control almost all industrial processes. ( more that 95% of closed-loop industrial processes.) * Minorsky (1922) “Directional stability of automatically steered bodies”, J. Am. Soc. Naval Eng., 34, p.284. وضعیت تاریخی

Lecture 18 Ali Karimpour Nov The standard form PID are: PID Controllers Proportional only: Proportional plus Integral: Proportional plus derivative: Proportional, integral and derivative: کنترلر PID

Lecture 18 Ali Karimpour Nov Lead-lag Compensators Closely related to PID control is the idea of lead-lag compensation. The transfer function of these compensators is of the form: If a p) in other form. If a>1 this is a lead network. Or (z<p) in other form. کنترلر پیش فاز پس فاز

Lecture 18 Ali Karimpour Nov A phase Lag network So it is a Lag network یک شبکه پس فاز R1R1 R2R2 C E1E1 + - E2E2 + -

Lecture 18 Ali Karimpour Nov R1R1 R2R2 C E1E1 E2E A phase Lead network یک شبکه پیش فاز So it is a Lead network